There is no difference in the phasers, but in the situations. The one time Khan gets hit by surprise, the other time he sees the attack coming.
When Kirk storms the bridge of the USS Vengeance together with Khan and Scotty, they take take out the whole crew except for the Commander. Kirk then gives Scotty a sign by nodding at him, after which Scotty fires a phaser burst at the unsuspecting Khan, taking him completely by surprise.
Khan is out cold. Is he really, though?
That is exactly what Kirk and Scotty planned prior to the attack:
KIRK: The minute we get to the bridge, drop him.
SCOTTY: What? Stun him? Khan? I thought he was helping us!
KIRK: I am pretty sure we are helping him.
Khan is not prepared for this surprise attack from the people who he thought to be working with him.
I believe that is the main difference to the other incident you mention, the fight on the floating barge:
While Uhura teleports in behind Khan, he still becomes aware of her presence in time to turn around and engage her.
He sees her pointing the phaser at him and is able to physically and mentally prepare for the attack. This is enough for the genetically improved Khan to withstand multiple phaser shots without being knocked down. It still has a severe effect on him and allows Spock to finally overpower him.
(Screenshots and Transcript taken directly from the movie)